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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 974284, 8 pages
A Proper-Orthogonal Decomposition Variational Multiscale Approximation Method for a Generalized Oseen Problem
Department of Mathematics, North Carolina A & T State University, Greensboro, NC 27411, USA
Received 6 June 2013; Accepted 25 October 2013
Academic Editor: Yinnian He
Copyright © 2013 John Paul Roop. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Borggaard, A. Duggleby, A. Hay, T. Iliescu, and Z. Wang, “Reduced-order modeling of turbulent flows,” in Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS '08), 2008.
- T. Iliescu and Z. Wang, “Variational multiscale proper orthogonal decomposition: convection-dominated convection-diffusion-reaction equations,” Mathematics of Computation, vol. 82, no. 283, pp. 1357–1378, 2013.
- T. Iliescu and Z. Wang, “Variational multiscale proper orthogonal decomposition: Navier-Stokes equations,” Numerical Methods for Partial Differential Equations. In press.
- V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, vol. 5, Springer, Berlin, Germany, 1986.
- J. Burkardt, M. Gunzburger, and H.-C. Lee, “POD and CVT-based reduced-order modeling of Navier-Stokes flows,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 1–3, pp. 337–355, 2006.
- M. D. Gunzburger, J. S. Peterson, and J. N. Shadid, “Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 4–6, pp. 1030–1047, 2007.
- J. Wang, Y. Wang, and X. Ye, “A robust numerical method for Stokes equations based on divergence-free finite element methods,” SIAM Journal on Scientific Computing, vol. 31, no. 4, pp. 2784–2802, 2009.